This study investigated young children's ability to solve probability problems and studied the cognitive processes proposed by Piaget and Inhelder as necessary to solve probability problems. The effects of tutorial and self-discovery training were measured and discussed. Results from 168 first-graders in five training conditions indicated that: (1) tutorial training methods were superior to self-discovery methods; (2) cognitively transitional children performed better than non-transitional children; (3) children demonstrated temporally stable and generalized performance increments following training; and (4) the Genevan view of probability solution was not supported. (Author/PK)